Pregunta
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10. [0/1 Points] DETAILS MY NOTES TGEIALG6 5.4.040. Find the degree of the polynomial. SUBMIT ANSWER

Ask by Wells Bradley. in the United States
Jan 24,2025

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To find the degree of a polynomial, arrange the terms in order of highest to lowest exponent and identify the term with the largest exponent. For example, in \(4x^3 - 2x^2 + 7x - 5\), the degree is 3.

Solución

Sure, I'd be happy to help you determine the degree of a polynomial. However, I'll need the specific polynomial expression to provide an accurate answer. **In the meantime, here's a general overview:** ### What is the Degree of a Polynomial? - **Definition:** The degree of a polynomial is the highest power of the variable \( x \) in the polynomial expression when it's written in its standard form (from highest to lowest degree). ### How to Find the Degree: 1. **Write the Polynomial in Standard Form:** Arrange the terms in descending order of the exponents of \( x \). *Example:* \[ 4x^3 - 2x^2 + 7x - 5 \] 2. **Identify the Highest Exponent:** Look for the term with the largest exponent. *In the example above*, the highest exponent is **3** (from \( 4x^3 \)). 3. **Determine the Degree:** The highest exponent is the degree of the polynomial. *So, the degree is **3***. ### Example Problem: Find the degree of the polynomial \( 6x^5 - 3x^3 + x - 8 \). **Solution:** 1. The polynomial is already in standard form. 2. The exponents are 5, 3, 1, and 0. 3. The highest exponent is 5. **Degree:** 5 --- **Please provide the specific polynomial** you're working with, and I'd be glad to help you find its degree!

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Bonus Knowledge

To find the degree of a polynomial, you need to identify the term with the highest exponent. For example, in the polynomial \(3x^4 + 2x^3 - x + 7\), the term \(3x^4\) has the highest exponent, which is 4. Therefore, the degree of this polynomial is 4! Another fun thing to remember is that if a polynomial has all its terms with the same degree, it is termed a "homogeneous polynomial." For example, \(5x^3 + 2y^3 - 4z^3\) would be a homogeneous polynomial of degree 3. So, not only can polynomials vary in degree, but they can also share the same degree across all their terms!

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